same mesh (edit mode) boolean intersection gives an error
Since no answers were added, I add one of my own to help others that like me, without reding the manual, may be stuck understanding how this kind of boolean works:

as MrZak and Nghillaz pointed out, I was selecting both part of the mesh, hoping that the "intersect (boolean)" edit-mode command would find an intersection in the selected geometry. 

Instead, the assumption is that you only select one of the mesh part that are supposed to be part of the intersection, not both.

See how it works, really:



The default behaviour is to do a boolean difference, but on the left side operation panel you can tweak the mode at your like.